1. Field of the Invention
The present invention relates to a method of fabricating an X-ray mask and a method of fabricating a semiconductor device with an X-ray mask fabricated by this method.
2. Description of the Background Art
In proximity X-ray exposure, an X-ray mask and a wafer formed with a resist film are arranged in proximity to each other, for executing X-ray irradiation. In this case, the X-ray mask is prepared from a membrane mask having an X-ray absorber pattern formed on an X-ray transmitter. The wafer is irradiated with X-rays through this membrane mask. Thus, an optical image is formed on the resist film with the X-rays transmitted through the X-ray transmitter portion of the membrane mask.
At this time, atoms forming the resist film absorb the X-rays. Thus, the resist film generates secondary electrons, thereby causing chemical change on molecules forming the resist film. A latent image of a pattern corresponding to the pattern of the X-ray transmitter portion of the membrane mask is formed on the resist film due to the chemical change.
Thereafter the resist film is developed by removing either the latent image portion or a portion other than the latent image portion. Thus, the pattern of the X-ray absorber portion of the membrane mask is transferred to the resist film.
The resolution R of the pattern formed on the resist film decided by the optical image is expressed as follows:R=k√{square root over ( )}(λ×G)where k represents a constant depending on the resist process or the like, λ represents the exposure wavelength, and G represents the distance between the surface of the X-ray mask and the surface of the resist film formed on the wafer. The distance G is hereinafter referred to as a mask-to-resist interval.
When a membrane mask having a mask-to-resist interval G of 10 μm is employed, exposure is currently performed with light having an exposure wavelength λ in the range of 0.7 nm to 1.2 nm. If the pattern formed on the membrane mask to be transferred to the resist film is about 60 nm, the resolution R of the transferred pattern satisfies a prescribed criterion. In order to further improve the resolution R, the exposure wavelength λ or the mask-to-resist interval G may be reduced.
If the mask-to-resist interval G is reduced, however, the X-ray mask and the resist film disadvantageously come into contact with each other, to increase the danger of breakage of the X-ray mask. Further, the mask-to-resist interval G cannot be extremely reduced due to a setting error included therein.
If the exposure wavelength λ is reduced, the energy of secondary electrons generated in the resist film due to X-ray irradiation is increased to disadvantageously reduce the resolution R.
A method of improving the resolution R of a pattern with a conventional X-ray mask under prescribed conditions of an exposure wavelength λ and a mask-to-resist interval G is now described.
A principle of forming an optical image with an X-ray phase-shift mask improving resolution R without changing an exposure wavelength λ and a mask-to-resist interval G is described with reference to FIG. 1. This principle is described in Jpn. J. Appl. Phys., Vol. 38 (1999) pp. 7076–7079 by K. Fujii, K. Suzuki and Y. Matsui, December, 1999.
FIG. 1 is a diagram for illustrating the effect of an X-ray phase-shift mask 1 having a line-and-space pattern (hereinafter referred to as “L & S pattern”) formed by alternately arranging openings provided with no X-ray absorbers and shielding portions provided with X-ray absorbers.
In the X-ray phase-shift mask 1, X-ray absorbers 2 are provided beneath an X-ray transmitter 3, as shown in FIG. 1. In general, X-rays are substantially absorbed by the X-ray absorbers 2 and substantially transmitted through the X-ray transmitter 3. Therefore, consider X-ray intensity levels on a point P of a resist film located immediately under an opening between a pair of adjacent X-ray absorbers 2 and a point Q of the resist film located immediately under a shielding portion consisting of one of the X-ray absorbers 2.
FIG. 1 illustrates optical images formed by X-rays transmitted through the openings with solid lines and those formed by X-rays transmitted through the shielding portions with dotted lines. As understood from FIG. 1, the X-rays transmitted through the openings form optical images not only immediately under the openings but also immediately under the shielding portions. Therefore, the resolution R of the X-ray phase-shift mask 1 is reduced.
In practice, however, the X-rays transmitted through the openings and those transmitted through the shielding portions are superposed with each other to form the optical images. In order to improve the optical image contrast, therefore, the X-ray phase shift-mask 1 must be so formed that the X-rays transmitted through the openings and the shielding portions respectively strengthen the optical images at the point P and weaken the optical images at the point Q.
Conditions for improving the optical image contrast are now described. It is assumed that tabs denotes the phase shift quantity of X-rays transmitted through the X-ray absorbers 2 and φgeo denotes geometric phase difference of X-rays resulting from difference between optical paths D→P and C→P. In this case, X-rays (B→D→P) transmitted through the openings and X-rays (A→C→P) transmitted through the shielding portions strengthen each other under the following condition:φgeo+φabs=0  (1)
At the point Q, X-rays (B→D→Q) transmitted through the openings and X-rays (A→C→Q) transmitted through the shielding portions weaken each other under the following condition:φgeo−φabs=π  (2)
Therefore, the optimum phase condition corresponding to both conditions of the expressions (1) and (2) is expressed as follows:λgeo=−φabs=0.5π
The optical image contrast is defined as (Ip−Iq)/(Ip+Iq), where Ip represents the intensity of X-rays on portions of the resist film located immediately under the openings, and Iq represents intensity of X-rays on portions of the resist film located immediately under the shielding portions.
It is assumed that X-ray intensity at the point P resulting from X-rays transmitted through the openings is 1, and X-ray intensity at the point Q resulting from X-rays transmitted through the openings is expressed as a. The X-ray intensity at the point P resulting from X-rays transmitted through the shielding portions is 1/MC times the X-ray intensity at the point P resulting from X-rays transmitted through the openings.
Therefore, X-ray intensity at the point Q resulting from the X-rays transmitted through the shielding portions is expressed as a/MC, where MC represents the mask contrast corresponding to the inverse number of the transmittance of the X-ray absorbers 2.
Under the aforementioned conditions, the optical image contrast in the optimum phase condition is expressed as follows:((1+2a/MC)−|1/MC−2a|)/((1+2a/MC)+|1/MC−2a|))
Further, the optical image contrast reaches the maximum value 1 when 2a=1/MC, which is the condition for obtaining an ideal optical image.
The aforementioned prior art Jpn. J. Appl. Phys., Vol. 38 (1999) by K. Fujii, K. Suzuki and Y. Matsui describes the following:
Consider a case of an exposure wavelength λ of 0.78 nm, a mask-to-resist interval G of 12 μm and mask contrast MC of 2.5, for example. In this case, the phase shift quantity φabs reaches 0.54π in an X-ray mask employing tantalum (Ta) films of 290 nm in thickness as X-ray absorbers 2 in an L & S pattern having a pitch of 70 nm.
Consider a case of an exposure wavelength λ of 0.78 nm, a mask-to-resist interval G of 7 μm and mask contrast MC of 2. In this case, the phase shift quantity φabs reaches 0.57π in an X-ray mask employing molybdenum (Mo) films of 370 nm in thickness as X-ray absorbers 2 in an L & S pattern having a pitch of 50 nm.
Problems related to an X-ray mask implementing the aforementioned optimum phase condition are described. The prior art describes an X-ray phase-shift mask 1 employing X-ray absorbers 2 having mask contrast MC of either 2 or 2.5 satisfying the optimum phase condition. This prior art further describes that the resolution R can be improved with respect to different mask-to-resist intervals G without changing the exposure wavelength λ.
In order to improve the resolution R, it is also effective to reduce the exposure wavelength λ, as hereinabove described. However, the aforementioned prior art describes no method of improving the resolution R by reducing the exposure wavelength λ without changing the mask-to-resist interval G in order to avoid a risk such as breakage of the mask.
In-practice, tungsten and tantalum generally employed as the materials for the X-ray absorbers 2 have absorption edges, i.e., boundaries of wavelengths capable of absorbing X-rays, of 0.69 nm and 0.73 nm respectively. In order to satisfy the condition φabs =−0.5π, therefore, the mask contrast MC must be increased also as to a wavelength slightly shorter than that of an X-ray absorption edge. Consequently, no X-rays are transmitted through the X-ray absorbers 2. Thus, the degree of contribution of the phase shift effect is reduced, to reduce the optical image contrast.
When the mask contrast MC is about 2 to 3 similarly to a general one, it follows that the phase shift quantity φabs of the X-ray absorbers 2 approaches zero from −0.5π. In this case, the optimum phase condition cannot be implemented. When a pattern is transferred with a wider mask-to-resist interval G which the geometric phase difference φgeo does not satisfy the optimum phase condition, the resolution R of the pattern is deteriorated.
In the conventional X-ray mask, the optical image contrast reaches the maximum value 1 when 2a=1/MC. However, the value a is decided by the size of the pattern formed on the X-ray mask, the exposure wavelength λ of X-rays and the mask-to-resist interval G.
In practice, the ideal state of the optical image contrast 1 cannot be implemented unless the mask contrast MC satisfies 2a=1/MC after the size of the pattern formed on the X-ray mask, the exposure wavelength λ of X-rays and the mask-to-resist interval G are decided.
When X-ray absorbers 2 constituted of a single substance are employed as in the prior art, the phase shift quantity φabs and the mask contrast MC are unequivocally decided. Therefore, the mask contrast MC does not necessarily satisfy the condition 2a=1/MC.
While various X-ray masks have been developed in order to solve the aforementioned problems, there has been developed no X-ray mask capable of further improving the resolution of a pattern of a semiconductor device formed with the X-ray mask.